Module p224_64

Autogenerated: ‘src/ExtractionOCaml/word_by_word_montgomery’ –lang Rust –inline p224 64 ‘2^224 - 2^96 + 1’ mul square add sub opp from_montgomery to_montgomery nonzero selectznz to_bytes from_bytes one msat divstep divstep_precomp curve description: p224 machine_wordsize = 64 (from “64”) requested operations: mul, square, add, sub, opp, from_montgomery, to_montgomery, nonzero, selectznz, to_bytes, from_bytes, one, msat, divstep, divstep_precomp m = 0xffffffffffffffffffffffffffffffff000000000000000000000001 (from “2^224 - 2^96 + 1”)

NOTE: In addition to the bounds specified above each function, all functions synthesized for this Montgomery arithmetic require the input to be strictly less than the prime modulus (m), and also require the input to be in the unique saturated representation. All functions also ensure that these two properties are true of return values.

Computed values: eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256

Structs

fiat_p224_montgomery_domain_field_element

The type fiat_p224_montgomery_domain_field_element is a field element in the Montgomery domain. Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]

fiat_p224_non_montgomery_domain_field_element

The type fiat_p224_non_montgomery_domain_field_element is a field element NOT in the Montgomery domain. Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]

Functions

fiat_p224_add

The function fiat_p224_add adds two field elements in the Montgomery domain.

fiat_p224_addcarryx_u64

The function fiat_p224_addcarryx_u64 is an addition with carry.

fiat_p224_cmovznz_u64

The function fiat_p224_cmovznz_u64 is a single-word conditional move.

fiat_p224_divstep

The function fiat_p224_divstep computes a divstep.

fiat_p224_divstep_precomp

The function fiat_p224_divstep_precomp returns the precomputed value for Bernstein-Yang-inversion (in montgomery form).

fiat_p224_from_bytes

The function fiat_p224_from_bytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order.

fiat_p224_from_montgomery

The function fiat_p224_from_montgomery translates a field element out of the Montgomery domain.

fiat_p224_msat

The function fiat_p224_msat returns the saturated representation of the prime modulus.

fiat_p224_mul

The function fiat_p224_mul multiplies two field elements in the Montgomery domain.

fiat_p224_mulx_u64

The function fiat_p224_mulx_u64 is a multiplication, returning the full double-width result.

fiat_p224_nonzero

The function fiat_p224_nonzero outputs a single non-zero word if the input is non-zero and zero otherwise.

fiat_p224_opp

The function fiat_p224_opp negates a field element in the Montgomery domain.

fiat_p224_selectznz

The function fiat_p224_selectznz is a multi-limb conditional select.

fiat_p224_set_one

The function fiat_p224_set_one returns the field element one in the Montgomery domain.

fiat_p224_square

The function fiat_p224_square squares a field element in the Montgomery domain.

fiat_p224_sub

The function fiat_p224_sub subtracts two field elements in the Montgomery domain.

fiat_p224_subborrowx_u64

The function fiat_p224_subborrowx_u64 is a subtraction with borrow.

fiat_p224_to_bytes

The function fiat_p224_to_bytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order.

fiat_p224_to_montgomery

The function fiat_p224_to_montgomery translates a field element into the Montgomery domain.

Type Aliases

fiat_p224_i1

fiat_p224_i1 represents values of 1 bits, stored in one byte.

fiat_p224_i2

fiat_p224_i2 represents values of 2 bits, stored in one byte.

fiat_p224_u1

fiat_p224_u1 represents values of 1 bits, stored in one byte.

fiat_p224_u2

fiat_p224_u2 represents values of 2 bits, stored in one byte.